3/4d+4=1/2d+18

Solution for 3/4d+4=1/2d+18 equation:

3/4d+4=1/2d+18

We move all terms to the left:

3/4d+4-(1/2d+18)=0


Domain of the equation: 4d!=0

d!=0/4

d!=0

d∈R



Domain of the equation: 2d+18)!=0

d∈R


We get rid of parentheses

3/4d-1/2d-18+4=0

We calculate fractions


6d/8d^2+(-4d)/8d^2-18+4=0

We add all the numbers together, and all the variables

6d/8d^2+(-4d)/8d^2-14=0

We multiply all the terms by the denominator


6d+(-4d)-14*8d^2=0

Wy multiply elements

-112d^2+6d+(-4d)=0

We get rid of parentheses

-112d^2+6d-4d=0

We add all the numbers together, and all the variables

-112d^2+2d=0

a = -112; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-112)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-112}=\frac{-4}{-224}
=1/56
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-112}=\frac{0}{-224}
=0
$